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DOE OSTI2022

Rates and Reversibilities in Interconnected Reaction Networks

Mathematical relations prescribing unidirectional forward and reverse rates originally derived based on single-path reaction sequences do not apply to interconnected reaction networks. The presence of branches in reaction networks, leading to alternative stable products, decreases unidirectional rates in reference to those calculated by single-path functional forms, as shown by simulated isotopic exchange rates, but impacts the unidirectional forward and reverse rates equally such that the functional form of effective reversibility remains unchanged. Regardless of stoichiometric numbers and network connectivity, the application of the pseudo-steady-state hypothesis on reactive intermediates in conjunction with consideration of unidirectional rates toward the product of interest and all alternative stable products results in mathematical expressions that accurately reflect simulated isotopic exchange rates. Further analyses based on kinetic resistance, a property akin to electrical resistance, illustrate the manifestation of nodal resistances in addition to the single-path kinetic resistance for interconnected reaction networks. The generalized formalism for assessing rates and reversibilities in interconnected networks derived herein enables us to demonstrate that unidirectional rates cannot be assessed solely from effective reversibilities and net rates of generation of stable species in such networks. Furthermore, isotopic exchange rates, under the condition that each elementary step in the overall reaction sequence forms a unique reactive intermediate that is consumed solely by the subsequent step, can be utilized to determine unidirectional rates and can serve to validate postulated reaction pathways in highly interconnected reaction networks (e.g., CO x hydrogenation).

42 ENGINEERING↗

DOE OSTI2020

Deciphering a Reaction Network for the Switchable Production of Tetrahydroquinoline or Quinoline with MOF-Supported Pd Tandem Catalysts

A mechanistic study of heterogeneous tandem catalytic systems is crucial for understanding and improving catalyst activity and selectivity but remains challenging. Here, we demonstrate that a thorough mechanistic study of a multistep reaction can guide us to the controllable selective synthesis of phenyltetrahydroquinoline or phenylquinoline with easily accessible precursors. The one-pot production can be achieved, catalyzed by a well-defined, bifunctional metal–organic framework-supported Pd nanoparticles, with only water as the side product. Our mechanistic study identifies six transient intermediates and ten transformation steps from the operando magic angle spinning nuclear magnetic resonance study under 27.6 bar H 2 . In particular, reactive intermediate 2-phenyl-3,4-dihydroquinoline cannot be observed with conventional chromatographic techniques but is found to reach the maximal concentration of 0.11 mol L –1 under the operando condition. The most probable reaction network is further deduced based on the kinetic information of reaction species, obtained from both operando and ex situ reaction studies. This deep understanding of the complex reaction network enables the kinetic control of the conversions of key intermediate, 2-phenyl-3,4-dihydroquinoline, with the addition of a homogeneous co-catalyst, allowing the selective production of tetrahydroquinoline or quinoline on demand. Finally, the demonstrated methods in this work open up new avenues toward efficient modulation of reactions with a complex network to achieve desired selectivities.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Engineering grain boundary anisotropy to elucidate grain growth behavior in alumina

Current grain growth models have evolved to account for the relationship between grain boundary energy/mobility anisotropy and the five degrees of grain boundary character. However, the role of grain boundary networks on overall growth kinetics remains poorly understood. To experimentally investigate this problem, a highly textured Al 2 O 3 was fabricated by colloidal casting in a strong magnetic field to engineer a unique spatial distribution of grain boundary character. Microstructural evolution was quantified and compared to an untextured sample. From this comparison, a prevalence of (0001)/(0001) terminated grain boundaries with anisotropic networks were identified in the textured sample. These boundaries and their networks were found to be driving grain growth at a faster rate than predicted by models. These findings will allow better modelling of grain growth in real systems by experimentally exploring the impact thereon of grain boundary plane anisotropy and relative energy/mobility differences between neighboring boundaries.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Fe-single-atom catalyst nanocages linked by bacterial cellulose-derived carbon nanofiber aerogel for Li-S batteries

Li-S battery (LSB) is promising for achieving high capacity. Still, its development is hindered by the complex redox process with sluggish kinetics and particularly the resulting lithium polysulfides (LiPS) shuttle effects. Single-atom catalysts (SACs), with their maximized atom utilization, could effectively chemisorb soluble LiPSs and expedite the sulfide conversion reaction kinetics. Here we report incorporating Fe single metal atom catalyst (Fe-SAC) in the sulfur cathode design and its electrocatalytic effects. Fe-doped ZIF-8 nanocages were introduced into a cheap biomass bacteria cellulose. A pyrolysis process converted them into an aerogel structure with Fe-SAC-functionalized N-doped carbon nanocages linked by a carbon nanofiber network (FeSA-NC@CBC), which was applied as a scaffold to fabricate freestanding and binder-free sulfur cathodes. He we conducted electrochemical measurements to reveal Fe-SAC functions including lowering energy barriers for S 8 reduction to liquid-phase LiPSs and further to solid-phase Li 2 S 2 /Li 2 S and accelerating Li 2 S 2 /Li 2 S nucleation and deposition, as corroborated by our theoretical calculation results. Benefiting from the synergistic effects of highly active Fe-SAC and three-dimensional conductive network, the sulfide reaction kinetics is improved, which can diminish LiPS shuttle effects and therefore improve LBS rate performance and cycling stability. Accordingly, the fabricated FeSA-NC@CBC composite cathode delivers an excellent rate capability at 2C with a reversible capacity of 840 mAh/g and a long-term cyclic stability of 800 mAh/g at 1C after 500 cycles.

25 ENERGY STORAGE↗

DOE OSTI2024

Enhancing Lattice Kinetic Schemes for Fluid Dynamics with Lattice-Equivariant Neural Networks

A new class of equivariant neural networks is presented, hereby dubbed lattice-equivariant neural networks (LENNs), designed to satisfy local symmetries of a lattice structure. The approach develops within a recently introduced framework aimed at learning neural network-based surrogate models’ lattice Boltzmann collision operators. Whenever neural networks are employed to model physical systems, respecting symmetries and equivariance properties has been shown to be key for accuracy, numerical stability, and performance. Here, hinging on ideas from group representation theory, trainable layers are defined whose algebraic structure is equivariant with respect to the symmetries of the lattice cell. In this work, the presented method naturally allows for efficient implementations, in terms of both memory usage and computational costs, supporting scalable training/testing for lattices in two spatial dimensions and higher (in which the size of symmetry group grows). The approach is validated and tested considering 2D and 3D flowing dynamics, both in laminar and turbulent regimes. It is compared with group-averaged-based symmetric networks and with plain, nonsymmetric, networks, showing how the presented approach unlocks the (a posteriori) accuracy and training stability of the former models and the train/inference speed of the latter networks. (LENNs are about one order of magnitude faster than group-averaged networks in 3D.) The work in this paper opens toward practical use of machine learning-augmented lattice Boltzmann CFD in real-world simulations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Explicit physics-informed neural networks for nonlinear closure: The case of transport in tissues

In upscaling methods, closures for nonlinear problems present a well-known challenge. While a number of theoretical methods have been proposed for handling such closures, nonlinearities still remain a significant obstacle for many problems. In this work, we use a combination of formal upscaling and data-driven machine learning for explicitly closing a nonlinear transport and reaction process in multiscale tissues. The classical effectiveness factor model is used to formulate the macroscale reaction kinetics. We train a multilayer perceptron network using training data generated by direct numerical simulations over microscale examples. Once trained, the network is used in an algorithm for numerically solving the upscaled (coarse-grained) differential equation describing mass transport and reaction in two example tissues. The network is described as being explicit in the sense that the network is trained using macroscale concentrations and gradients of concentration as components of the feature space rather than incorporating them as part of a constraint in the optimization process. Network training and solutions to the macroscale transport equations were computed for two different tissues. The two tissue types (brain and liver) exhibit markedly different geometrical complexity and spatial scale (cell size and sample size). The upscaled solutions for the average concentration are compared with numerical solutions derived from the microscale concentration fields by a posteriori averaging. There are three outcomes of this work of particular note. 1) Our overall approach results in an upscaled nonlinear PDE. The PDE is closed using a neural network, and our approach results in the definition of the classical effectiveness factor for effecting closure. 2) We identify particular source terms for the closure problem that are important for representing the structure of the closure. These source terms involve macroscale concentrations and their gradients. We adopt these source terms to use as explicit features in the learning algorithm. We find the trained networks that include the macroscale source terms generate models that are able to predict the correction factor with increased fidelity over those that do not. 3) We find that the trained network exhibits good generalizability, and it is able to predict the effectiveness factor with high fidelity for realistically-structured tissues despite the significantly different scale and geometrical complexity of the two example tissue types. This latter result emphasizes our purposeful connection between conventional averaging methods with the use of machine learning for closure; this contrasts with some machine learning methods for upscaling where the exact form of the macroscale equation remains unknown.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Degrees of Rate Control in Interconnected Reaction Networks

Overall reactions in interconnected networks exhibit net, forward, and reverse rates that are governed by both constitutive elementary steps in the pathway of interest and branching elementary steps that lead to alternative products. Accordingly, steps in branching pathways exhibit negative net, forward, and reverse degrees of rate control, as they reduce reaction flux to the desired product. We here contextualize the forward and reverse degrees of rate control in terms of kinetic resistances (inverse of rates) and leverage the additive nature of kinetic resistance to decouple kinetic driving forces contributed by constitutive elementary steps and branching points (nodal species) in interconnected networks. Regardless of the network connectivity, forward and reverse degrees of rate control are shown to converge at equilibrium. Away from equilibrium, we identify two critical features of interconnected networks: stoichiometric regularity─condition where all stoichiometric numbers are unity─and pathway symmetry around nodal species─condition where branching pathways share the same rate constants, stoichiometry, and species concentrations/activities─that result in (i) equal forward, reverse, and consequently net degrees of rate control and (ii) forward and reverse degrees of rate control that exhibit constant offsets, respectively, across all extents of reaction. Furthermore, our discourse further provides a mathematical description for the influence of stoichiometric irregularity and pathway asymmetry on forward and reverse degrees of rate control. Altogether, the presented work details the effects of network (inter)connectivity and stoichiometry on reaction kinetics and, in doing so, establishes general protocols for capturing these effects as additive terms in the formulation of forward and reverse degrees of rate control.

10 SYNTHETIC FUELS↗

DOE OSTI2023

Reversible Reactions, Mesh Size, and Segmental Dynamics Control Penetrant Diffusion in Ethylene Vitrimers

The diffusion of two aromatic dyes with nearly identical sizes was measured in ethylene vitrimers with precise linker lengths and borate ester cross-links using fluorescence recovery after photobleaching (FRAP). One dye possessed a reactive hydroxyl group, while the second was inert. The reaction of the hydroxyl group with the network is slow relative to the hopping times of the dye, resulting in a large slowdown by a factor of 50 for a reactive probe molecule. A kinetic model was fit to the fluorescence intensity data to determine rate constants for the reversible reaction of the dye from the network, which confirms the role of slow reaction kinetics. A second network cross-linker was also investigated with a substituted boronic ester showing ∼10,000 times faster exchange kinetics. In this system, the two dyes show the same diffusion coefficient, as the reaction is no longer the rate-limiting step. The role of dense meshes on small and large dyes is also discussed in the context of the existing theories. Finally, these results highlight the potential of dynamic networks to control penetrant transport through synergistic effects of the mesh size, dynamic bond kinetics, and penetrant–network interactions.

confinement↗

NASA NTRS2001

Combining Flux Balance and Energy Balance Analysis for Large-Scale Metabolic Network: Biochemical Circuit Theory for Analysis of Large-Scale Metabolic Networks

Predicting behavior of large-scale biochemical metabolic networks represents one of the greatest challenges of bioinformatics and computational biology. Approaches, such as flux balance analysis (FBA), that account for the known stoichiometry of the reaction network while avoiding implementation of detailed reaction kinetics are perhaps the most promising tools for the analysis of large complex networks. As a step towards building a complete theory of biochemical circuit analysis, we introduce energy balance analysis (EBA), which compliments the FBA approach by introducing fundamental constraints based on the first and second laws of thermodynamics. Fluxes obtained with EBA are thermodynamically feasible and provide valuable insight into the activation and suppression of biochemical pathways.

Beard, Daniel A.↗

DOE OSTI2022

Path sampling of recurrent neural networks by incorporating known physics

Recurrent neural networks have seen widespread use in modeling dynamical systems in varied domains such as weather prediction, text prediction and several others. Often one wishes to supplement the experimentally observed dynamics with prior knowledge or intuition about the system. While the recurrent nature of these networks allows them to model arbitrarily long memories in the time series used in training, it makes it harder to impose prior knowledge or intuition through generic constraints. In this work, we present a path sampling approach based on principle of Maximum Caliber that allows us to include generic thermodynamic or kinetic constraints into recurrent neural networks. We show the method here for a widely used type of recurrent neural network known as long short-term memory network in the context of supplementing time series collected from different application domains. These include classical Molecular Dynamics of a protein and Monte Carlo simulations of an open quantum system continuously losing photons to the environment and displaying Rabi oscillations. Our method can be easily generalized to other generative artificial intelligence models and to generic time series in different areas of physical and social sciences, where one wishes to supplement limited data with intuition or theory based corrections.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2024

A graph neural network-state predictive information bottleneck (GNN-SPIB) approach for learning molecular thermodynamics and kinetics

Molecular dynamics simulations offer detailed insights into atomic motions but face timescale limitations. Enhanced sampling methods have addressed these challenges but even with machine learning, they often rely on pre-selected expert-based features. Here, in this work, we present a Graph Neural Network-State Predictive Information Bottleneck (GNN-SPIB) framework, which combines graph neural networks and the state predictive information bottleneck to automatically learn low-dimensional representations directly from atomic coordinates. Tested on three benchmark systems, our approach predicts essential structural, thermodynamic and kinetic information for slow processes, demonstrating robustness across diverse systems. The method shows promise for complex systems, enabling effective enhanced sampling without requiring pre-defined reaction coordinates or input features.

Zou, Ziyue↗

DOE OSTI2025

Physics-Informed Neural Network (PINN) Prediction of Mixed Mass-Heat-Crystallization Limited Methane Hydrate Formation and Dissociation in Micro-Confinement

The creation and use of Physics-Informed Neural Networks (PINNs) for simulating the dynamics of methane hydrate formation and dissociation will be presented. The PINN framework's main benefit is its capacity to impose physical consistency with only a partial comprehension of the governing equations. This makes the algorithm especially useful for systems with little experimental evidence or a lack of theoretical knowledge. A strong basis for forecasting methane hydrate behavior over the verified operating ranges of 30.0-80.9 bar pressure and 1.0-4.0 K sub-cooling conditions is provided by the combination of conductive heat transfer equations and mixed mass-transfer–crystallization kinetics. PINNs were more accurate at predicting the mixed mass-heat-crystallization limited kinetics than conventional Artificial Neural Networks (ANNs), demonstrating remarkable predictive accuracy for methane hydrate production over the ANN model. The efficiency of incorporating physical limitations from first principles into machine learning frameworks for methane hydrate crystallizations is reinforced by these findings. For hydrate-related applications in energy generation, carbon sequestration, and climate modelling, our study establishes PINNs as a computational tool that is both scalable and efficient. The proven capacity to close the gap between conventional physics-based simulations and solely data-driven models creates new opportunities for expedited hydrate research and practical applications.

Hartman, Ryan L [NYU Tandon School of Engineering]↗

DOE OSTI2021

A Nickel-Decorated Carbon Flower/Sulfur Cathode for Lean-Electrolyte Lithium–Sulfur Batteries

Lithium–sulfur (Li–S) batteries involve a reversible conversion reaction between sulfur and lithium sulfide (Li 2 S) via a series of soluble lithium polysulfide intermediates (LiPSs), enabling a high theoretical specific capacity of 1675 mAh g –1 . However, this process exhibits large polarization and low sulfur utilization and suffers critical capacity fade. The primary approach to tackle the problem has so far been to infiltrate sulfur into nanostructured carbon. Furthermore, most studies using porous carbon as host materials have tested with high electrolyte to sulfur ratios (E/S) (generally > 15 µL mg –1 ) that compromise the cell-level energy density. Here, a flower-shaped porous carbon structure with nickel nanoparticles that can address the problems discussed above is designed. First, the 3D flower-shaped carbon structure enables short ionic transport lengths. Second, the small pore diameters <10 nm and high specific surface areas > 3300 m 2 g –1 with sufficient pore volume are ideal for charging performance for low E/S ratios. Finally, Ni nanoparticles are employed onto the flower-shaped network to improve the reaction kinetics. Collectively, it is successfully demonstrated that the batteries with a high mass loading of 5 mg cm –2 and a 5 µL mg –1 E/S ratio can retain cycle retention of 70% after 150 cycles.

25 ENERGY STORAGE↗

DOE OSTI2021

A persistent adjoint method with dynamic time-scaling and an application to mass action kinetics

In this article, we consider an optimization problem where the objective function is evaluated at the fixed-point of a contraction mapping parameterized by a control variable, and optimization takes place over this control variable. Since the derivative of the fixed-point with respect to the parameter can usually not be evaluated exactly, an adjoint dynamical system can be used to estimate gradients. Using this estimation procedure, the optimization algorithm alternates between derivative estimation and an approximate gradient descent step. We analyze a variant of this approach involving dynamic time-scaling, where after each parameter update the adjoint system is iterated until a convergence threshold is passed. Here, we prove that, under certain conditions, the algorithm can find approximate stationary points of the objective function. We demonstrate the approach in the settings of an inverse problem in chemical kinetics, and learning in attractor networks.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Mesoporous optically clear heat insulators for sustainable building envelopes

Mesoporous materials exhibit highly controlled nanoscale structures, often templated by liquid crystalline assemblies of surfactants, with emergent and often designable physical properties. However, scaling their fabrication to be suitable for uses like envelopes of buildings is challenging. Here we describe fabrication of flexible square-meter-sized films and multi-centimeter-thick slabs made of three-dimensional spatial graphs of mesopore tubes having all structural features under 50 nanometers. Solution-based kinetic fabrication process templates growing networks of cylindrical surfactant micelles with thin tubes of polysiloxane forming gel networks and, upon replacing surfactants and solvents with air, yields lightweight materials with >99% visible-range optical transparency and ~10 mW K-1m-1 thermal conductivity. Such predesigned metamaterials enable transparent thermal barriers for wall-grade insulated glass units, square-meter window retrofits and unconcentrated solar thermal energy harnessing.

14 SOLAR ENERGY↗

DOE OSTI2022

Autoencoder Neural Network for chemically reacting systems

Incorporating detailed chemical kinetic models is critical for accurate simulations of reacting flows. However, detailed models involve a large number of thermochemical (TC) state variables. Solving the governing equations to evolve these TC variables becomes impractical for real-world applications. In this work, we propose an autoencoder (AE) neural network (NN)-based reduced model to accelerate such simulations. The AE NN is first trained to find a low-dimensional latent representation of the TC states. Then, the evolving state of a chemical system can be tracked by solving the equations of the latent variables instead of the original TC equations. We demonstrate the reduced model in a syngas CO/H 2 combustion system, using training data collected from canonical perfectly stirred reactors (PSRs). It is found that the AE model can reduce the dimension of the combustion system from 12 to 2 while maintaining low reconstruction error and excellent elemental mass conservation for the test dataset. In the a posteriori test, the combustion states obtained from solving the two latent equations are compared to those from solving the 12 equations of the full model. The AE reduced method is found to be able to capture the diverse combustion states on the top two branches of the S-curve well including the extinction turning point, but with higher prediction errors for states near the ignition turning point.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Data for Selective Oxidation of 3-Hydroxypropionic Acid to Malonic Acid over Pd/C: Mechanistic and Kinetic Study

Malonic acid (MA) is a high-value dicarboxylic acid with strong industrial demand, yet its current production heavily relies on petrochemical feedstocks. Here, we report the first systematic study for the sustainable production of MA via oxidation of 3-hydroxypropionic acid (3-HP) with a Pd/Carbon catalyst. The effects of oxidant type (O2 and H2O2), pH, and temperature on the reaction chemistry were comprehensively evaluated. Guided by experimental observation and DFT-calculated thermochemical energetics, reaction networks for 3-HP oxidation with both oxidants are proposed and validated through kinetic modeling. MA was identified as the primary oxidation product, while further oxidation yields acetic acid and oxalic acid. The kinetic model validated the network, displaying excellent agreement (R2 > 0.95). Kinetic observations also enabled a direct comparison between O2 and H2O2 and revealed their distinct behaviors. The model was further developed into a temperature-time map, providing insight into conditions that maximize MA production. Malonic acid selectivity of 56.9 % and yield of 50.5 % were achieved at 3 bar oxygen, equimolar NaOH:3-HP ratio, and 50 °C.

Bioproducts↗

DOE OSTI2026

Data and code from: Selective oxidation of 3-hydroxypropionic acid to malonic acid over Pd/C: Mechanistic and kinetic study

3-Hydroxypropionic Acid↗